We consider the propositional logic equipped with Chellas stit operators for a finite set of individual agents plus the historical necessity modality. We settle the question of whether such a logic enjoys restricted interpolation property, which requires the existence of an interpolant only in cases where the consequence contains no Chellas stit operators occurring in the premise. We show that if action operators count as logical symbols, then such a logic has restricted interpolation property iff the number of agents does not exceed three. On the other hand, if action operators are considered to be nonlogical symbols, then the restricted interpolation fails for any number of agents exceeding one. It follows that unrestricted Craig interpolation also fails for almost all versions of stit logic.

中文翻译：

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STIT 逻辑中的受限插值及其缺失

我们认为命题逻辑配备切拉斯斯蒂特有限个体代理集合的算子加上历史必要性模态。我们解决了这样一个逻辑是否具有受限插值属性的问题，它仅在结果不包含前提中出现的 Chellas stit 算子的情况下才要求存在插值。我们表明，如果动作运算符算作逻辑符号，那么当代理的数量不超过三个时，这样的逻辑具有限制的插值特性。另一方面，如果动作运算符被认为是非逻辑符号，那么限制插值对于任何数量超过一个的代理都会失败。因此，对于几乎所有版本的 stit 逻辑，不受限制的 Craig 插值也失败了。